A holonomy characterisation of Fefferman spaces. (English) Zbl 1298.53041
Fefferman spaces that provide a geometric relationship between CR geometry and conformal geometry are studied. It is prove that some Fefferman spaces, associated to CR structures of special type, are completely characterized by the existence of a parallel orthogonal complex structure on the standard tractor bundle. This fact can be equivalently reformulated in the terms of conformal holonomy.
Reviewer: Mihail Banaru (Smolensk)
MSC:
| 53C29 | Issues of holonomy in differential geometry |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53A40 | Other special differential geometries |
Keywords:
CR structure; Fefferman space; parallel orthogonal complex structure; standard tractor bundle; conformal holonomyReferences:
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